NetHack has a lot of ways to gain Luck during the game, which affects a lot of mechanics. Some thoughts on adjustments to Luck, taken from http://nethackwiki.com/wiki/Luck
-2 Break a mirror. (Other glass items have no effect on Luck.)
-n Breaking n eggs laid by you (at worst -5).
+1 Sitting on a throne (sometimes).
0 Throwing a worthless gem at a unicorn.
-1 to +1 Throwing unknown valuable gem at cross-aligned unicorn.
-3 to +3 Throwing known valuable gem at cross-aligned unicorn.
+1 Throwing unknown valuable gem at co-aligned unicorn.
+2 Throwing named valuable gem at co-aligned unicorn.
+5 Throwing identified valuable gem at co-aligned unicorn.
-1 Hitting a blind floating eye (1 in 500 chance).
-1 Jumping in Sokoban.
-1 Breaking a boulder in Sokoban.
-1 Casting stone-to-flesh on a Sokoban boulder.
-1 Polymorphing a Sokoban boulder.
-1 Reading a scroll of earth in Sokoban.
-1 Being pulled by a thrown iron ball in Sokoban.
-1 Hurtling through the air in Sokoban due to Newton's 3rd Law. (i.e. throwing something while levitating)
-1 Squeezing past a boulder in Sokoban (or walking over one when polymorphed into a giant)
-1 Killing a tame monster.
-1 Killing a peaceful monster (sometimes). See note below.
-2 Killing a peaceful human, and you are not chaotic. ("You murderer!")
-5 Killing a co-aligned unicorn.
-5 to -2 Cannibalism (eating your own species), unless an orc or a caveman.
Set to 0 Praying with negative regular luck (sometimes: "golden glow" boon).
-3 Praying on wrong altar.
-3 Praying before your prayer timeout has expired.
-5 A sacrifice (not your own race) on Moloch's altars in Gehennom.
-3 Being converted by trying to convert an altar.
-1 Otherwise unsuccessful at converting altar.
+1 Successfully converting an altar.
-1 Sacrificing at another god's altar.
-1 Kicking another god's altar ("Thou shalt pay, infidel!")
-1 Trying to engrave something on another god's altar (also gives "Thou shalt pay, infidel!")
+2 Sacrificing your own race on your own chaotic altar.
-2 Sacrificing your own race on Moloch's altar.
-5 Sacrificing your own race, you aren't chaotic.
-1 Sacrificing an unidentified fake Amulet of Yendor.
-3 Sacrificing an identified fake Amulet of Yendor.
+1 Sacrificing, slightly mollifying your god, negative luck.
Set to 0 Sacrificing, mollifying your god, negative luck.
+1 Sacrificing, having a hopeful feeling, negative luck.
Set to 0 Sacrificing, reconciling, negative luck.
0 to +5 Sacrificing, god happy.
Note about luck penalty for killing peaceful monsters, from :
If you manage to kill a peaceful monster without angering it, you have a 50% chance of losing one point of Luck. This is in addition to the Luck penalty for murder described above and the penalty of -5 Luck for killing a unicorn of your own alignment. However, simply killing a peaceful monster with one whack from a melee weapon will anger it before it dies, avoiding this penalty. Most wands and spells will also anger a monster even if they kill it in one zap, but "beam" attacks such as striking or polymorph have a chance of killing without angering, and incurring the additional penalty.
Obviously a lot of those may not have true application to a DCC tabletop game, but there's a few ideas in there, in particular throwing gems at unicorns, sacrificing to the Gods (in NetHack, via corpses, but DCC tabletop could be monetary donations as well), etc.